Upper bound for outer general position number after vertex removal

Let $G$ be a graph and let $x$ be a vertex that is not a cut vertex of $G$. Write ${\rm gp}_{\rm o}(G)$ for the outer general position number of $G$ and $\deg_G(x)$ for the degree of $x$ in $G$. Upper-bound conjecture. If $x$ is not a cut vertex of $G$, then

$${\rm gp}_{\rm o}(G-x) \le {\rm gp}_{\rm o}(G) + \deg_G(x).$$

This would provide a general upper bound for the change in outer general position number under deletion of a non-cut vertex. Together with the preceding lower-bound theorem for vertices lying in an outer general position set, it would constrain how vertex removal affects ${\rm gp}_{\rm o}(G)$; the supplied text does not indicate whether the proposed bound is known or remains open.